To live, operate, or function with the unyielding belief in something, especially that which is fanciful, unrealistic, or untrue. Primarily heard in US. Jeremy's always labored under the illusion of being a great writer, even though he's never written more than a few crummy poems. No one likes paying taxes, but those who would call for them to be done away with altogether are laboring under the illusion that our society can function without them!